Question

Asked Dec 13, 2019

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A population has a mean μ=83 and a standard deviation σ=2424.

Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64.

Step 1

Given data

Mean μ=83

Standard Deviation σ=24

**Points on sampling distribution of the sample mean:**

- If the true population distribution of a random variable, say,
*x*, is normal with parameters, mean*μ*and standard deviation*σ*, then, whatever be the size (*n*) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean*μ*and standard deviation*σ/√n*. - Even if the true population distribution of a random variable, say,
*x*, is not normal and has population mean*μ*, standard deviation*σ*, then, for a large size (*n*≥ 30) of a sample taken from the population, the distribution of the sample mean is approximately normal, with parameters, mean*μ*and standard devia...

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